and extract the time-optimal pulse duration \(T_*\Omega _{\mathrm {max}}= 7.612\)  for the CZ gate. The form of the fitting function is motivated by the observation that \(1-F\)  should vanish in the first order of \(T-T_*\) , otherwise negative gate errors would be possible for \(T>T_*\) . The resulting time-optimal pulse is about 10% faster then the pulse in Ref. [1]} with \(T\Omega _{\mathrm {max}}= 8.58536\) , showing a relevant speedup of the gate. Our results also show that the duration of the pulse in Ref. [1]} is already quite close to the achievable minimum.
